No. Negligible. The purpose of vector designs is scalability, there should be no reason for 0.1px to be better or worse for the quality of your image inin Illustrator.
Yes. Pixels are a unit of measurement and are rasterized according to the dpi settings in illustrator. 300 pixels per inch for example. A) the 0.1px stroke should translate relatively clean with respect to the output size from illustrator, and B) if someone were to blow up that image and pixelate it, it would distort all of the pixels not just your line. So it isn't ignored per se, but again for relevant purposes, negligible.
Chris Bolseng
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